Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 180 · 40 sums

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

1. 1.What is 37²? =
2. 2.How many whole numbers lie between 7² and 8²?
3. 3.How many whole numbers lie between 48² and 49²?
4. 4.What is the smallest whole number by which 162 must be divided to get a perfect square?
5. 5.Which of these is a perfect square? (a) 486 (b) 489 (c) 484
6. 6.Which of these is a perfect square? (a) 361 (b) 365 (c) 362
7. 7.What is the smallest whole number by which 117 must be divided to get a perfect square?
8. 8.A square garden has an area of 1681 square m. How long is each side (in m)?
9. 9.What is the smallest whole number by which 8 must be divided to get a perfect square?
10. 10.What is √2116? =
11. 11.A square garden has an area of 441 square m. How long is each side (in m)?
12. 12.What is 80²? =
13. 13.Which of these is a perfect square? (a) 543 (b) 561 (c) 529
14. 14.How many whole numbers lie between 44² and 45²?
15. 15.What is √2704? =
16. 16.A square garden has an area of 900 square m. How long is each side (in m)?
17. 17.Which of these is a perfect square? (a) 111 (b) 100 (c) 112
18. 18.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
20. 20.How many whole numbers lie between 8² and 9²?
21. 21.What is 22²? =
22. 22.What is the smallest whole number by which 126 must be divided to get a perfect square?
23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
24. 24.What is √2209? =
25. 25.A square garden has an area of 2601 square m. How long is each side (in m)?
26. 26.Which of these is a perfect square? (a) 216 (b) 196 (c) 210
27. 27.What is √289? =
28. 28.How many whole numbers lie between 15² and 16²?
29. 29.What is √6889? =
30. 30.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
31. 31.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
32. 32.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
33. 33.What is 45²? =
34. 34.What is 12²? =
35. 35.What is √1296? =
36. 36.A square garden has an area of 256 square m. How long is each side (in m)?
37. 37.A square garden has an area of 625 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 22² and 23²?
39. 39.What is 72²? =
40. 40.How many whole numbers lie between 23² and 24²?

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